No captions Captions Stop the video above first if it is playing.
No captions Captions Stop the video above first if it is playing.
Sasha and Keoni notice patterns in the equations they have derived for parabolas with the same p-values for different vertices. They predict an equation for a parabola with a p-value of 3 and a vertex at (7, 2).
Episode Supports
Students’ Conceptual Challenges
Keoni initially thinks the distance from a general point to the directrix (y = –1) is y – 1 [3:48]. Sasha questions this [3:58]. Keoni explains that he was only looking at the label of the directrix when he labeled the distance [4:06].
➤ Together, they point out the distances of y, 1, and y + 1. Using the coordinate grid, they make sense of the three lengths of the sides of the triangle [4:14-5:54].
Focus Questions
For use in a classroom, pause the video and ask these questions:
1. [Pause video at 1:27]. How does Keoni know that his point is a “special point”?
2. [Pause video at 8:11]. Why did Keoni multiply out the (y – 5)2 and the (y +1)2 terms but leave the (x – 7)2 unchanged?
Supporting Dialogue
Provide opportunities to for students to revoice mathematical thinking. Ask a few students to revoice the ideas used in this episode:
1. Revoice how you can determine the lengths of the sides of the triangle.
2. Revoice how Sasha and Keoni solved for y [8:14- 8:59].
Math Extensions
1. Try deriving the equation of another parabola using the methods of this episode. Derive the equation for a parabola with a p-value of 3 and a vertex of (–4, 1).
2. Show your work as you derive this equation. Label your focus and directrix as well as the lengths of the sides of the right triangle.
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